A note on the integrality of volumes of representations

Kim, Sungwoon

doi:10.1090/proc/16472

A note on the integrality of volumes of representations
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by Sungwoon Kim;

Proc. Amer. Math. Soc. 151 (2023), 4949-4960

DOI: https://doi.org/10.1090/proc/16472

Published electronically: June 30, 2023

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Abstract:

Let $\Gamma$ be a torsion-free, non-uniform lattice in $\mathrm {SO}(2n,1)$. We present an elementary, combinatorial–geometrical proof of a theorem of Bucher, Burger, and Iozzi [Math. Ann. 381 (2021), pp. 209–242] which states that the volume of a representation $\rho :\Gamma \to \mathrm {SO}(2n,1)$, properly normalized, is an integer if $n$ is greater than or equal to $2$.

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Proceedings of the American Mathematical Society

A note on the integrality of volumes of representations
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Abstract: